Elastic behaviour (II)
If the axially loaded faces do not deform, then clearly it must be those at an angle to the loading axis that do, the diagonal faces. And because they are at an angle to the loading axis they will bend.
The bending of each face beams must be symmetrical about the mid-point of the face and can be estimated using beam bending theory. To do this each face is described as two beams, cantilevered at the vertices of the hexagonal cell and loaded at the centre point. Note that one beam (i.e. a half cell wall) is pushed upward, the other downward.
This [derivation] gives the Young modulus of the honeycomb as
\[E = \frac{4}{{\sqrt 3 }}{E_{\rm{S}}}{\rm{ }}{\left( {\frac{t}{l}} \right)^3}\]
Using the measured values of t( = 0.09 mm) and l ( = 6.30 mm) and taking ES as 70 GPa, the elastic modulus is predicted to be 471 kPa. This is within 10% of the measured value for the sample.
The predominant contribution to the Young modulus is therefore from the bending of the diagonal faces.